where
\(\frac{1}{h}K(\frac{x_{\rm j}-(\tilde{p}_{\rm i})_{\rm j}}{h}) \equiv K_{h}(x_{\rm j},(\tilde{p}_{\rm i})_{\rm j})\)  is a user-specified
kernel function, \(w_{\rm 1},w_{\rm 2},...,w_{\rm N}\)  is a set of
normalized weights giving the observations different importance in the
estimation if needed (if not, \(w_i=1/n\)  for all \(i\) ), and \(h\)  is a
hyper-parameter of KDE called the bandwidth or smoothing parameter
[1]}. This hyper-parameter may be interpreted as the
standard deviation of the selected kernel. The definition in
Eq. (REF ) has been simplified with respect to other
definitions given in the literature by taking the multivariate kernel
as the product of \(D\)  one-dimensional kernels, and replacing the
bandwidth matrix \(H\)  by \(h^2 I\)  (where \(I\)  is the identity matrix).
